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ICA 2015: Progress in Automation, Robotics and Measuring Techniques pp 113–126Cite as

Decomposition and Parallelization of Linear Programming Algorithms

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 350))

Abstract

The paper assesses possible approaches to decomposition and parallelization of basic linear programming algorithms, including: Dantzig-Wolfe, Benders, augmented Lagrangian, revised simplex and primal-dual interior point methods. Quite surprisingly, the first three of them - of hierarchical optimization type - exhibit considerable advantages nowadays, in the era of multicore processors and accelerators of any type (GPU, FPGA, Xeon Phi, etc.).

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References

  1. Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4, 238–252 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bertsekas, D.P.: Constrained Optimization and Lagrange Multiplier Methods. Academic Press, Boston (1982)

    MATH  Google Scholar 

  3. Bertsekas, D.P., Tsitsiklis, J.N.: Parallel and Distributed Computation: Numerical Methods. Prentice-Hall, Englewood Cliffs (1989)

    MATH  Google Scholar 

  4. Bertsimas, D., Tsitsiklis, J.N.: Introduction to Linear Optimization. Athena Scientific, Belmont (1997)

    Google Scholar 

  5. Bixby, R.E.: Solving Real-World Linear Programs: A Decade and More of Progress. Operations Research 50, 3–15 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bixby, R.E., Cook, W., Cox, A., Lee, E.K.: Computational Experience with Parallel Mixed Integer Programming in Distributed Environment. Annals of Operations Research 90, 19–43 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bixby, R.E., Martin, A.: Parallelizing the Dual Simplex Method. INFORMS Journal on Computing 12, 45–56 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bixby, R.E., Rothberg, E.: Progress in computational mixed integer programming - A look back from the other side of the tipping point. Annals of Operations Research 149, 37–41 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Dantzig, G.B., Wolfe, P.: Decomposition Principle for Linear Programs. Operations Research 8, 101–111 (1960)

    Article  MATH  Google Scholar 

  10. Fourer, R.: Linear Programming Software Survey. OR/MS Today 40(3) (2013)

    Google Scholar 

  11. Gass, S.I.: Linear programming: methods and applications. McGraw-Hill, New York (1969)

    Google Scholar 

  12. Geoffrion, A.M., Graves, G.W.: Multicommodity Distribution System Design by Benders Decomposition. Management Science 20, 822–844 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gondzio, J., Sarkissian, R.: Parallel interior-point solver for structured linear programs. Math. Program. 96, 561–584 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  14. Gondzio, J., Grothey, A.: Exploiting structure in parallel implementation of interior point methods for optimization. Comput. Manag. Sci. 6, 135–160 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  15. Hall, J.A.J.: Towards a practical parallelisation of the simplex method. Computational Managment Science 7, 139–170 (2010)

    Article  MATH  Google Scholar 

  16. Illés, T., Terlaky, T.: Pivot versus interior point methods: Pros and cons. European Journal of Operational Research 140, 170–190 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  17. Kiwiel, K.C.: Methods of Descent for Nondifferentiable Optimization. Springer, Berlin (1985)

    MATH  Google Scholar 

  18. Lübbecke, M.E., Desrosiers, J.: Selected Topics in Column Generation. Operations Research 53, 1007–1023 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  19. Ruszczyński, A.: Regularized decomposition and augmented Lagrangian decomposition for angular linear programming problems. In: Lewandowski, A., Wierzbicki, A. (eds.) Aspiration Based Decision Support Systems. Lecture Notes in Economics and Mathematical Systems, vol. 331, pp. 80–91. Springer, Berlin (1989)

    Chapter  Google Scholar 

  20. Vanderbeck, F., Wolsey, L.A.: Reformulation and Decomposition of Integer Programs. In: Jünger, M., Liebling, T.M., Naddef, D., Nemhauser, G.L., Pulleyblank, W.R., Reinelt, G., Rinaldi, G., Wolsey, L.A. (eds.) 50 Years of Integer Programming 1958–2008, pp. 431–502. Springer, Heidelberg (2010)

    Google Scholar 

  21. Yarmish, G., Van Slyke, R.: A distributed, scaleable simplex method. Journal of Supercomputing 49, 373–381 (2009)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Control and Computation Engineering, Warsaw University of Technology, Warsaw, Poland

    Andrzej Karbowski

  2. NASK, Research and Academic Computer Network, Warsaw, Poland

    Andrzej Karbowski

Authors
  1. Andrzej Karbowski
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Correspondence to Andrzej Karbowski .

Editor information

Editors and Affiliations

  1. Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland

    Roman Szewczyk

  2. Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland

    Cezary Zieliński

  3. Industrial Research Institute Automation and Measurements PIAP, Warsaw, Poland

    Małgorzata Kaliczyńska

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Karbowski, A. (2015). Decomposition and Parallelization of Linear Programming Algorithms. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Progress in Automation, Robotics and Measuring Techniques. ICA 2015. Advances in Intelligent Systems and Computing, vol 350. Springer, Cham. https://doi.org/10.1007/978-3-319-15796-2_12

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  • DOI: https://doi.org/10.1007/978-3-319-15796-2_12

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15795-5

  • Online ISBN: 978-3-319-15796-2

  • eBook Packages: EngineeringEngineering (R0)

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